The Oracle of Arithmetic

Quanta ^ | 28 Jun, 2016 | Erica Klarreich

[MtnClimber]

At 28, Peter Scholze is uncovering deep connections between number theory and geometry. In 2010, a startling rumor filtered through the number theory community and reached Jared Weinstein. Apparently, some graduate student at the University of Bonn in Germany had written a paper that redid “Harris-Taylor” — a 288-page book dedicated to a single impenetrable proof in number theory — in only 37 pages. The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry.

“It was just so stunning for someone so young to have done something so revolutionary,” said Weinstein, a 34-year-old number theorist now at Boston University. “It was extremely humbling.”

Mathematicians at the University of Bonn, who made Scholze a full professor just two years later, were already aware of his extraordinary mathematical mind. After he posted his Harris-Taylor paper, experts in number theory and geometry started to notice Scholze too.

Since that time, Scholze, now 28, has risen to eminence in the broader mathematics community. Prize citations have called him “already one of the most influential mathematicians in the world” and “a rare talent which only emerges every few decades.” He is spoken of as a heavy favorite for the Fields Medal, one of the highest honors in mathematics.

Scholze’s key innovation — a class of fractal structures he calls perfectoid spaces — is only a few years old, but it already has far-reaching ramifications in the field of arithmetic geometry, where number theory and geometry come together.

[Do the math]

My paper in analytic geometry has just been accepted, just need to make a few minor changes. After solving that particular problem, it made me think of at least ten new problems. Math is a never ending story. Number theory , to me, is the most difficult type of mathematics. I love mathematics.

[Arlis]

Blessed beyond words.......3 daughters as well, one just graduated from UVA with Distinction (all A’s while there last 2 years), Phi Beta Kappa - degree in Linguistics - she’s fluent in Spanish and Portuguese - as I am..........another a VERY successful realtor making the big bucks.....

And if in town, they all are usually home for Sunday night dinner!

Most importantly, all are strong Christians......

[AllAmericanGirl44]

bkmk

[SunkenCiv]

---

· String Theory Ping List ·

---

---

· Join · Bookmark · Topics · Google ·
· View or Post in 'blog · post a topic · subscribe ·

---

[LibWhacker]

Gödel's incompleteness theorem: no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., an algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. (Wiki)

Furthermore, given there are some theorems that are so difficult they will in all likelihood never be proven -- even though they are true -- new mathematical methods will continue to be developed for as long as men are alive.

[DennisR]

Well, we really do not need a balanced budget per se. We need a LIMITED, balanced budget. In other words, the Feds take, say, 10% of our combined incomes - that is all they will be allowed to spend. If you use the “balanced budget” approach, they will just raise our taxes again to “balance the budget.”

[DennisR]

All well and good, but what is the practical application of this mathematical breakthrough? Just wondering...

[AdmSmith]

Thanks for the link, it takes more than some rainy days during the summer to read this. Perhaps it is better to start with this http://www.math.uni-bonn.de/people/scholze/CDM.pdf

[AdmSmith]

The text is very technical, but a good basic introduction is the 6 videos by Alan Macdonald starting with this https://www.youtube.com/watch?v=9qEST41kG6Q ...

then a few years study ...

and then off to https://www.youtube.com/watch?v=X2j2Md2DEBU

However, a good non-technical history of Mathematics is this 50 minutes video by John Dersch https://www.youtube.com/watch?v=YsEcpS-hyXw

[AdmSmith]

Sorry, the lecture starts at lecture 0 https://www.youtube.com/watch?v=srwoPQfWWS8

[Chode]

thx... will watch as time permits

[SunkenCiv]

Thanks AdmSmith.

[ckilmer]

You are an impressive man going and coming. kudos.

[Arlis]

No, but my kids are. Credit goes to their mom.....my still-beautiful-at-70, size 4 wife (after 8 kids) who was #1 in her large HS class.......

BTW - she didn’t want any children...... ;-)

You are kind.